A characterization of Gorenstein Hilbert functions in codimension four with small initial degree

Details A characterization of Gorenstein Hilbert functions in codimension four with small initial degree A characterization of Gorenstein Hilbert functions in codimension four with small initial degree

2007-03-29

arxiv.org/abs/math/0703901v2

Math. Res. Lett. 15 (2008), 331-349

Mathematics

Commutative Algebra

A few changes. Final version, to appear in Math. Res. Lett

Scientific paper

The main goal of this paper is to characterize the Hilbert functions of all (artinian) codimension 4 Gorenstein algebras that have at least two independent relations of degree four. This includes all codimension 4 Gorenstein algebras whose initial relation is of degree at most 3. Our result shows that those Hilbert functions are exactly the so-called {\em SI-sequences} starting with (1,4,h_2,h_3,...), where $h_4 \leq 33$. In particular, these Hilbert functions are all unimodal. We also establish a more general unimodality result, which relies on the values of the Hilbert function not being too big, but is independent of the initial degree.

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